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PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and Z. Bittnar
Numerical Analysis of Ductility in Reinforced Concrete Beams in the CASTEM 2000
M.P. Barbosa and A.L. Gamino
Department of Civil Engineering, São Paulo State University, Ilha Solteira, Brazil
M.P. Barbosa, A.L. Gamino, "Numerical Analysis of Ductility in Reinforced Concrete Beams in the CASTEM 2000", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 117, 2002. doi:10.4203/ccp.75.117
Keywords: ductility, reinforced concrete beams, CASTEM 2000, numerical analysis, finite element method, concrete strength, longitudinal tension reinforced ratio, tensile reinforced ratio, spacing between stirrups, scale effect.
Ductility is the measure of the ability of a material, section, structural element or structural system of suffering inelastic strain in the neighbourhoods of a possible rupture, with no substantial loss of its resistant capacity. It is an important property conferred on structural elements concerning the capacity of redistribution of efforts at the action of differential settlements or seismic actions on the structure.
As it is known, for safety matters, it is necessary that the structures, in the imminence of a collapse, present evident alarm signs in the form of fissures and great strain. Such signs characterize the ductile rupture, contrarily to what happens in fragile structures .
In this work the global and local ductility indexes were numerically quantified in reinforced concrete beams, subject to the pure and simple flexion and with monotonous loads through the CASTEM 2000 calculation code, with the analysis of the influence of the following parameters on the ductility of the beams: concrete strength, longitudinal tension reinforced ratio, tensile reinforced ratio, spacing between stirrups, scale effect.
The CASTEM 2000 uses the method of the finite elements for structural analysis, the elastic – plastic model of Drucker-Prager to describe the rheology of the concrete, the elastic – plastic perfect model for the steel and the method of Newton- Raphson, commonly used for solution of non-linear systems.
The numerical evaluation of the ductility in structures of reinforced concrete was accomplished with a constitutive non-linear analysis based on the rheologic constituent laws of each material so that there would be a substantial proximity among the numerical and experimental answers providing reliability to the ductility indexes calculated through the numerical process.
Once the theoretical studies concerning the non-linear behaviour of structures of reinforced concrete were grounded, a problem of practical nature appears since structures manifesting a non-linear behaviour originate also non-linear systems of equations, whose solution is only possible with the application of increasing and iterative procedures . Within this field stands out the method of Newton-Raphson commonly used for the solution of non-linear systems whose main characteristic is to provide numerical solutions with reliability, convergence and stability properties as shown in the researches by Rubert , Proença , Barbosa , Merabet  and Boukari .
The numerical results reached show that the increase of the concrete strength, the decrease of the longitudinal tension reinforced ratio, the decrease of the tensile reinforcement ratio, the decrease of the spacing between stirrups and the enlargement of the scale effect provided increments in the global and local ductility indexes.
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